Homogeneous probability measures on the Cantor set
Probability
2021-08-25 v2 General Topology
Abstract
We show that every homeomorphism between closed measure zero subsets extends to a measure preserving auto-homeomorphism, whenever the Cantor set is endowed with a suitable probability measure. This is valid both for the standard product measure, as well as for the universal homogeneous rational measure.
Cite
@article{arxiv.1812.09565,
title = {Homogeneous probability measures on the Cantor set},
author = {W. Bielas and W. Kubiś and M. Walczyńska},
journal= {arXiv preprint arXiv:1812.09565},
year = {2021}
}
Comments
Some corrections, new subsection added, final version (18 pages)